LOCATIONAL MARGINAL PRICING APPROACH FOR A DEREGULATED ELECTRICITY MARKET

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1 LOCATIONAL MARGINAL PRICING APPROACH FOR A DEREGULATED ELECTRICITY MARKET A Abirami 1, T R Manikandan 2 1 PG scholar, Department of EEE, K.S.Rangasamy College of technology, Tiruchengode, Tamilnadu, India 2 Assistant Professor, Department of EEE, K.S.Rangasamy College of technology, Tiruchengode, Tamilnadu, India *** Abstract - In restructured electricity markets, an effective transmission pricing method is required to address transmission issues and to generate correct economic signals to reduce the generation cost. It is necessary to develop an appropriate pricing scheme Transmission Organization (RTO), to organize regional power systems to ensure non-discriminatory transmission services to generation companies (GENCO s) and bilateral transactions. In the restructured power industry open access is provided to the transmission system. Due to that can provide the useful information to market Transmission Open Access (TOA) the power flow in the users, such as generation companies, transmission companies and customers. These pricing depends on generator bids, load levels and transmission network constraints. Transmission line constraints can result in variations in energy prices throughout the network. The proposed approach is based on DC optimal power flow model with considering of losses. Resulting lines reach the power transfer limit and so it will leads to a condition known as congestion [1-2]. The congestion may be caused due to a mixture of reasons, such as transmission line outages, generator outages and change in energy demand. Transmission congestion has impact on the entire system as well as on the individual market participants i.e. sellers and buyers. Without congestion optimization problem is solved by Quadratic low cost GENCO s are used to meet the load demand but if Programming [QP] approach. Locational Marginal congestion is present in the transmission network then it Pricing methodology is used to determine the energy prevents the demand to be met by the lowest-priced price for transacted power and to manage the network resources due to mentioned transmission constraints and congestion and marginal losses. Variation of this leads to the allocation of higher price GENCO s. values with transmission constraint conditions also studied. Simulation is carried out on IEEE 30 bus test system and the results are presented. Key Words: Locational Marginal Pricing, Quadratic Programming (QP), DC Optimal Power Flow (DCOPF). 1. INTRODUCTION By Tradition, power industry is vertically integrated, in which the generation, Transmission and distribution are arranged collectively as a single utility to serve its customers. This will lead to the inefficient operation of power system. So the electric power industry has undergone deregulation around the world, a core tenet of which is to build an open-access, unambiguous and fair electricity markets [6]. Due to central operation of transmission and distribution system it will remain in a monopoly mode. Under the deregulated electricity `market environment, transmission networks play a vital role in supporting the transaction between producers and consumers. One drawback of transmission network is overloading. Federal Energy Regulatory Commission (FERC) willing to create non-profit organizations, called Independent System Operator System (ISO) and Regional There are two types of pricing methods are available in practice for congestion management [11]. They are uniform and non-uniform pricing structure. In this paper congestion is managed by means of Locational Marginal Pricing () i.e. non-uniform pricing structure. The at a location is defined as the marginal cost to supply an additional MW increment of power at the location without violating any system security limits [1]. This price reflects not only the marginal cost of energy production, but also its delivery. Because of the effects of both transmission losses and transmission system congestions, can vary significantly from one location to another. If the lowest priced electricity is allocated for all Location values at all nodes will be same. If congestion present in the system lowest cost energy cannot reach all location, more expensive generators will allocated to reach out the demand. In this situation values will be differ from one location to another. In pool-based electricity market ISO collects hourly supply and demand bids from Generator Serving Traders (GSTs) on behalf of GENCO s and Load Serving Traders (LSTs) on behalf of pool consumers [6]. ISO determines the generation and demand schedule as well as s based on increased social welfare maximization, subject to system operational and security constraints [9-11]. Mathematically, at any node in the system is the dual variable for the equality 2015, IRJET ISO 9001:2008 Certified Journal Page 348

2 constraint at that node [4]. Buyers in the market pays ISO based on their price for dispatched energy. The ISO pays sellers in the market based on their respective prices. The difference between two adjacent buses is the congestion cost which arises when the energy is transferred from one location to the other location. Marginal losses represent incremental changes in system losses due to incremental demand changes. Incremental losses yield additional costs which are referred to as the cost of marginal losses. Thus is the summation of the costs of marginal energy, marginal loss and congestion. can be stated as follows: = generation marginal cost + congestion cost + marginal loss cost is obtained from the result of Optimal Power Flow (OPF). Either AC-OPF or DC-OPF is used to determine the [7]. To reduce the complexity in the calculation in this paper DC-OPF is used. In DC-OPF only real power flow is considered [6]. Different types of optimization models are used for calculations like LP and Lagrangian relaxation using karush kuhn-tucker conditions. Evolutionary algorithm like genetic algorithm [12] is also used. Among these in this paper QP is used to solve the optimization problem. 1.1 Types of Bids Most commonly a generator bid varies with many factors, some of the factors are difficult to model. For simplicity generator bids are assumed to be equal to their incremental costs for perfect competition. There are two bidding models available in practice [12]. They are (1) Fixed generator bids (related to piecewise-linear heat rates) (2) Linear bids (related to quadratic heat rates). In this paper linear bids are used to calculate the generator offer price. Linear bid function is defined as a quadratic function and it is given by the following equation ) = + + ($/hr) (1) C i (PG i) - cost of generating i th unit a i b i - no-load cost - linear cost coefficient c i - quadratic cost coefficient of unit i. These coefficients are given by the generator manufacturer. 1.2 Day-Ahead and Real-Time Energy Markets Restructured power market consists of different types of market. An energy market is a place where the financial trading of electricity takes place. It naturally consists of a day-ahead market and real-time market, while the ancillary service markets are able to provide services such as synchronized reserve, regulation and reliable operation of transmission system. The day-ahead market is a type of forward market and runs on the day before the functioning day [1-2].Generation offers, demand bids, and bilateral transactions are accepted by the Day-Ahead market in the regulated market timeline. Virtual offers and bids are also received to increase the market liquidity. Load forecasting tool is used to predict the load in the submitted bids. As a result of running the optimization model the generation dispatch and electricity prices for each hour of the operating day was calculated. Normally, generated by the day-ahead market is called ex-ante, because the is calculated before the energy a transaction happens. In the real-time market, post- calculation will be performed as like that of ex-ante. Basically ex-ante will be same as that of post- if the forecasted load reflects the actual load in the real time market. In this paper Day-ahead market and ex-ante is considered. in the deregulated market depends on various factors such as low cost generator outage, transmission line outage, transmission line limits, load changes, demand bids and generation offers of consumers. In this paper we mainly focus on transmission line limit [4] and generation limit [5] as a constraint. The paper is structured as follows: Section 2 provides the existing transmission pricing method. Section 3 provides the problem formation. Section 4 presents the DC-OPF problem formations. Section 5 provides the Quadratic Programming method. Section 6 provides the results and analysis. Section 7 describes conclusion. 2. EXISTING TRANSMISSION PRICING METHOD Transmission pricing offer global access for all participants in the market. To recover the costs of transmission network and encourage market investment in transmission an understandable price structure is necessary. In this section various pricing methods and their calculations are discussed Postage-Stamp Rate Method Postage-stamp rate scheme is conventionally used by electric utilities to allot the permanent transmission price 2015, IRJET ISO 9001:2008 Certified Journal Page 349

3 between the users of firm transmission service. This method does not need power flow calculations and is independent of the transmission distance and system arrangement. This transmission pricing method allocates transmission charges based on the amount of the transacted power. For each transaction the magnitude of power transfer is calculated at the time of system peak Contract Path Method Contract path method also does not required power flow calculation. In this method contract path is a corporeal transmission pathway among two transmission users that disregards the fact that electrons follow corporeal paths that may differ dramatically from contract paths. Following to the specification of contract paths, transmission prices will then be assigned using a postagestamp rate, which is determined either individually for each of the transmission systems or on the average for the entire grid MW-Mile Method The MW-Mile Method is also called as line-by-line method since it considers, in its calculations, changes in MW transmission flows and transmission line lengths in miles. The method calculates charges associated with each wheeling transaction based on the transmission capacity use as a function of the magnitude of transacted power, the path followed by transacted power, and the distance traveled by transacted power. The MW-mile method is also used in identifying transmission paths for a power transaction. This method requires dc power flow calculations. The MW-mile method is the first pricing strategy proposed for the recovery of fixed transmission costs based on the actual use of transmission network. Total transmission capacity cost is calculated as follows: K - set of lines 3. PROBLEM FORMATION The main objective of this problem is minimization of total cost subjected to energy balance constraint and transmission constraint. Power flow is obtained by DCOPF model with considering of losses. In this OPF reactive power is ignored and the voltage magnitudes are assumed to be unity [7]. Objective function is given by Min (3) Subject to Generation limit constraint is given by Transmission line limit is given by i - Generator index n - Number of generators j - Line index C i - Cost of i th generator unit Pg i - Generation of i th generator unit (4) (5) (6) = TC * [2] Pg i min Pg i min - Minimum limit of generating unit - Maximum limit of generating unit TCt - cost allocated to transaction t TC - total cost of all lines in $ Lk - length of line k in mile ck - cost per MW per unit length of line k MWk - flow in line k, due to transaction t T - set of transactions Pd i - Demand of i th unit lf i min lf i max - minimum limit of line flow - maximum limit of line flow 4. FORMATION OF DC-OPF In AC network real and reactive power transmitted from the generating unit to load centre. Direct Current Optimal 2015, IRJET ISO 9001:2008 Certified Journal Page 350

4 Power Flow gives active Power Flow in AC network. This DCOPF is does not have convergence problem i.e. non iterative. From the accuracy level AC-OPF is better than DC-OPF. Power injection at a node and voltage angles are the important variables for DC-OPF. Active power injection at a bus is given by the Equation (7). Reactance between bus i and bus j (7) Power flow on the transmission line is given by the equation (8). = ( - ) (8) - Reactance of line i. DC-OPF equations and power flow in the branch relationship is represented by the Equation (9) & (10). Ѳ = P (9) Quadratic programming is a mathematical model to accomplish the finest outcome. This is one of the optimization techniques. It consists of quadratic objective function, subject to equality and inequality conditions in linear form. In the DCOPF with losses model optimization problem is formed as a Quadratic Programming problem. The method creates a sequence of quadratic programming problems that converge to the optimal solution of the original nonlinear problem. Comparing with the older algorithm which uses an augmented Lagrangian, the method has advantages in terms of CPU time and robustness. Quadratic Programming based optimization is involved in power systems for maintaining a desired voltage profile, maximizing power flow and minimizing generation cost. These quantities are generally controlled by complex power generation which is usually having two limits. Here minimization is considered as maximization can be determined by changing the sign of the objective function. Further, the quadratic functions are characterized by the matrices and vectors. Solving procedure for optimal power flow with Quadratic Programming approach using QP solver is explained in the Following algorithm. = (b x A) Ѳ (10) P N x 1 vector of bus active power injection for buses 1,..., N. B N x N admittance matrix with R=0. Ѳ N x 1 vector of bus voltage angle for buses 1,...,N. PL M x 1 vector of branch flows. M - Number of branches. b M x M vector diagonal susceptance matrix. A M x N bus branch incidence matrix. Starting and ending bus elements are 1 and -1 respectively. Otherwise 0. Earlier studies of calculations with the DCOPF ignore the line losses. Thus, the energy price and the congestion price follow a perfect linear model with a zero loss price. However, challenges arise if losses need to be considered to calculate the marginal loss component in the, especially considering the significance of marginal loss which may be up to 20% different among the different zones in the New York Control Area, based on actual data. 5. QUADRATIC PROGRAMMING Step1: Formation of quadratic objective function with linear equality and inequality constraint. Step2: Read the initial values for line and generator data. Also read the generator and line limits. Step3: Initialize the solution vector X. Step4:Formation of node arc incidence matrix to the system. Step5: Formation of B matrix. Step6: Obtain the matrix for power injection and line flow given in the equations (9) & (10) and objective function. Step7: Solve the obtained matrix by QP solver in the MATLAB. Step8: Get the value. 6. RESULTS AND ANALYSIS The proposed QP method simulation were developed using MATLAB 7.10 software package and the system configuration is Intel Core i3-2328m Processor with 2.20 GHz speed and 2 GB RAM.IEEE 30 bus system is used as a test system for this paper. This system consists of 41 lines, 6 generators. Line and generator data used for the simulation work. 2015, IRJET ISO 9001:2008 Certified Journal Page 351

5 Simulation is carried out with the help of MATLAB coding. Generator offer price is calculated by the linear bid function. For converting the $ into Indian rupee in these paper by simply assuming 1$ equal to 60 rupees. 6.1 Generator Data for 30 Bus System IEEE 30 bus system consists of 6 generators. Generator Data consist of maximum and minimum value of generation and cost coefficient values. Generator data for IEEE 30 bus system is given in table 1. Table 1 : Generator data for IEEE 30 bus system GENERATOR NO P i,min MW P i,max MW a i b i c i G G G G G G From the Table 1, it can be inferred that the does not varies when there is infinite transmission capacity. Case 2: is calculated using DC OPF without loss for the IEEE 30 bus system, with congestion is created by reducing the line 5 power flow upper limit from 45 MW to 0.3 MW. Table 3: values when congestion occurred Following three cases are considered for the values calculation and analysis of results. Case 1: values under normal condition Case 2: values when congestion occurred Case 3: values when losses occurred Case 1: is calculated using DCOPF without loss for the IEEE 14 bus system is calculated and presented in the table Table 2: values under normal condition Bus. No Bus. No , IRJET ISO 9001:2008 Certified Journal Page 352

6 From the Table 3, it can be inferred that the values varies with transmission congestion when any one of the transmission line gets overloading. Case 3: is calculated using DC OPF with considering of loss for the IEEE 30 bus system is presented in the Table 4. Table 4: values when Losses occurred From the table 4, it can be inferred that value is varied depends on any overloading transmission line condition. 7. CONCLUSION In a lot of restructured energy markets, the Locational Marginal Pricing acts as an important position in recent times. is looks set to be the most popular congestion management technique adopted by electricity markets around the world. To understand the determination of Loss DC Optimal power Flow is carefully analyzed which is the proposed technique in this paper. Constraints like transmission, generation and transmission line outages are used to analyze the market participants about the location value of electricity. also used to maintain the stable operation of transmission system without affect the buyers and sellers in the market. act as a true price signals for adding transmission capacity, generation capacity and future loads. It achieves its unique ambition of better effectiveness of power system operations in the short-term operational time frames by openly addressing the effects related with power transmission above the interconnected grid. We can extend our work with higher bus system and adding more constraints to our problem. Instead of DC-OPF, ACOPF can be used to solve the power flow problem. REFERENCES [1] Shahidehpour M, Yamin H, Li Z. Market operations in electric power systems. New York: Wiley; [2] Kirschen DS, Strbac G. Fundamentals of power system economics. Wiley; [3] A. J. Wood, B. F. Wollenberg, Power Generation, Operation and Control (second edition), John Wiley&Sons, New York, 1996 [4] Ricardo Fernández-Blanco, JoséM.Arroyo, and Natalia Alguacil, Network-Constrained Day-Ahead Auction for Consumer Payment Minimization IEEE transactions on power systems, vol. 29, no. 2, march [5 ] Mohammad Ebrahim Hajiabadia, Habib Rajabi Mashhadib decomposition: A novel approach for structural market power monitoring Electric Power Systems Research March [6] M. Murali, M. Sailaja Kumari, M. Sydulu, Optimal spot pricing in electricity market with inelastic load using constrained bat algorithm Electrical Power and Energy Systems 62 (2014) [7] K. Purchala, L. Meeus, D. Van Dommelen, and Belmans, Usefulness of DC Power Flow for Active Power Flow Analysis, Proc. of IEEE PES Annual Meeting 2005, pp , June , IRJET ISO 9001:2008 Certified Journal Page 353

7 [8] T. Overbye, X. Cheng, and Y. Sun, A Comparison of the AC and DC Power Flow Models for Calculations, Proceedings of the 37th Hawaii International Conference on System Sciences, [9] A. J. Conejo and J.A. Aguado, Multi-Area Coordinated Decentralized DC Optimal Power Flow, IEEE Trans. on Power Systems, vol. 13, no. 4, pp , Nov [10] Luonan Chen, Hideki Suzuki, Tsunehisa Wachi, Yukihir Shimura, Components of Nodal Prices for Electric Power Systems, IEEE Trans. on Power Systems, vol. 17, no. 1, pp , Feb [11] T.Orfanogianni and G. Gross, A General Formulation for, IEEE Trans. On Power Systems, vol. 22, no. 3, pp , Aug [12] Singh H, Hao S, Papalexopoulos A. Transmission congestion management in competitive electricity markets. IEEE Trans Power Syst 1998;13: , IRJET ISO 9001:2008 Certified Journal Page 354